Question 05 (e)

A ball is floating on the surface of the sea. The ball’s height (in m) above the sea floor at time (in s) is given by

Answer the questions below. Evaluate all function values and provide justification for your claims. Include units.

(e) Find the initial position of the ball and then determine what is the earliest time at which the ball is back in its initial position.

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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint

Note that if and only if .

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Solution

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Since , the initial position of the ball is .

Now, we want to find the first positive real number at which .

Note that is equivalent with and .

Therefore, our problem is reduced to find the first positive real number such that .

Using the Hint, if and only if .

This implies that , i.e., is the earliest time that the ball is back in its initial position.